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Find the missing number in the series: 2, 6, 12, 20, 30, ?
36
40
42
44
42
Recognize the series as a sequence of squares plus the number itself (n┬▓ + n) or identify the constant second difference of 2.
Recognize the series as a sequence of squares plus the number itself (n┬▓ + n) or identify the constant second difference of 2.
Analyze consecutive differences
Calculate the difference between consecutive terms: 6-2=4, 12-6=6, 20-12=8, 30-20=10. The differences are 4, 6, 8, 10, which forms an arithmetic progression with a common difference of 2.
Calculate the next term
Following the pattern of adding consecutive even numbers, the next difference must be 10 + 2 = 12. Adding this to the last term: 30 + 12 = 42.
Alternative pattern verification
The series follows the formula n┬▓ + n where n starts from 1: (1┬▓тБ║┬╣)=2, (2┬▓тБ║┬▓)=6, (3┬▓тБ║┬│)=12, (4┬▓тБ║тБ┤)=20, (5┬▓тБ║тБ╡)=30. Thus, for n=6, (6┬▓тБ║тБ╢) = 36+6 = 42.
A: 36 is the result of 6┬▓, failing to account for the +n addition. B: 40 ignores the required incremental pattern of the series. D: 44 results from adding 14 instead of 12, which deviates from the consistent +2 difference pattern.
C is correct because the series follows an incremental pattern of consecutive even numbers (4, 6, 8, 10, 12), and adding 12 to 30 yields 42.
If the differences between terms are increasing by a constant value, it is always a second-order arithmetic series; checking the double difference (2, 2, 2...) is the fastest way to confirm your logic.
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